The Appeal to the Consequences of a Belief is a fallacy that comes in
the following patterns:

X is true because if people did not accept X as being true then there would be negative consequences.

X is false because if people did not accept X as being false, then there would be negative consequences.

X is true because accepting that X is true has positive consequences.

X is false because accepting that X is false has positive consequences.

I wish that X were true, therefore X is true. This is known as Wishful Thinking.

I wish that X were false, therefore X is false. This is known as Wishful Thinking.

This line of "reasoning" is fallacious because the consequences of a belief have no bearing on whether the belief is true or false. For example, if someone were to say "If sixteen-headed purple unicorns don’t exist, then I would be miserable, so they must exist" it would be clear that this would not be a good line of reasoning. It is important to note that the consequences in question are the consequences that stem from the belief. It is important to distinguish between a rational reason to believe (RRB) (evidence) and a prudential reason to believe (PRB) (motivation). A RRB is evidence that objectively and logically supports the claim. A PRB is a reason to accept the belief because of some external factor (such as fear, a threat, or a benefit or harm that may stem from the belief) that is relevant to what a person values but is not relevant to the truth or falsity of the claim.

The nature of the fallacy is especially clear in the case of Wishful thinking. Obviously, merely wishing that something is true does not make it true. This fallacy differs from the Appeal to Belief fallacy in that the Appeal to Belief involves taking a claim that most people believe that X is true to be evidence for X being true.